Hierarchical Modeling of Longitudinal Trade Networks

The gravity model serves as a standard regression model of trade flow between countries. We present a simple longitudinal version of the model to represent trade flows between 136*135=18360 ordered pairs of countries from 1990-2000. While patterns of trade are certainly similar across pairs of countries, there is clear evidence that fitting one set of parameters for all pairs provides an overly simplistic representation of trade. On the other hand, the pair-specific data are too few to separately provide precise estimates of the pair-specific parameters. As a middle ground, we consider parameter estimation using a hierarchical factor model, which allows for complex differences across exporting and importing pairs of countries. Not only does this model allow for detection of country specific effects, but it also outperforms simpler estimation approaches in terms of out-of-sample prediction of trade.